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We develop a medium-size semi-structural time series model of inflation dynamics that is consistent with the view – often expressed by central banks – that three components are important: a trend anchored by long-run expectations, a Phillips curve and temporary fluctuations in energy prices. We find that a stable long-term inflation trend and a well identified steep Phillips curve are consistent with the data, but they imply potential output declining since the new millennium and energy prices affecting headline inflation not only via the Phillips curve but also via an independent expectational channel.

We evaluate the role of financial conditions as predictors of macroeconomic risk first in the quantile regression framework of Adrian et al. (2019b), which allows for non-linearities, and then in a novel linear semi-structural model as proposed by Hasenzagl et al. (2018). We distinguish between price variables such as credit spreads and stock variables such as leverage. We find that (i) although the spreads correlate with the left tail of the conditional distribution of GDP growth, they provide limited advanced information on growth vulnerability; (ii) nonfinancial leverage provides a leading signal for the left quantile of the GDP growth distribution in the 2008 recession; (iii) measures of excess leverage conceptually similar to the Basel gap, but cleaned from business cycle dynamics via the lenses of the semi-structural model, point to two peaks of accumulation of risks-the eighties and the first eight years of the new millennium, with an unstable relationship with business cycle chronology.

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A mixed-frequency semi-structural model is used for estimating unobservable quantities such as the output gap, the Phillips curve and the NAIRU in real time. We consider two specifications: in one the output gap is observed as the official CBO measure, in the other is unobserved and derived via minimal theory-based restrictions. We find that the CBO model implies a smoother trend output but the second model better captures the business cycle dynamics of nominal and real variables. The methodology offers both a framework for evaluating official estimates of unobserved quantities of economic interest and for tracking them in real time.